(125-x^3)=(5-x)(x^2+ax+b)

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Solution for (125-x^3)=(5-x)(x^2+ax+b) equation: 


Simplifying
(125 + -1x3) = (5 + -1x)(x2 + ax + b)

Remove parenthesis around (125 + -1x3)
125 + -1x3 = (5 + -1x)(x2 + ax + b)

Reorder the terms:
125 + -1x3 = (5 + -1x)(ax + b + x2)

Multiply (5 + -1x) * (ax + b + x2)
125 + -1x3 = (5(ax + b + x2) + -1x * (ax + b + x2))
125 + -1x3 = ((ax * 5 + b * 5 + x2 * 5) + -1x * (ax + b + x2))
125 + -1x3 = ((5ax + 5b + 5x2) + -1x * (ax + b + x2))
125 + -1x3 = (5ax + 5b + 5x2 + (ax * -1x + b * -1x + x2 * -1x))
125 + -1x3 = (5ax + 5b + 5x2 + (-1ax2 + -1bx + -1x3))

Reorder the terms:
125 + -1x3 = (5ax + -1ax2 + 5b + -1bx + 5x2 + -1x3)
125 + -1x3 = (5ax + -1ax2 + 5b + -1bx + 5x2 + -1x3)

Add 'x3' to each side of the equation.
125 + -1x3 + x3 = 5ax + -1ax2 + 5b + -1bx + 5x2 + -1x3 + x3

Combine like terms: -1x3 + x3 = 0
125 + 0 = 5ax + -1ax2 + 5b + -1bx + 5x2 + -1x3 + x3
125 = 5ax + -1ax2 + 5b + -1bx + 5x2 + -1x3 + x3

Combine like terms: -1x3 + x3 = 0
125 = 5ax + -1ax2 + 5b + -1bx + 5x2 + 0
125 = 5ax + -1ax2 + 5b + -1bx + 5x2

Solving
125 = 5ax + -1ax2 + 5b + -1bx + 5x2

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '-5ax' to each side of the equation.
125 + -5ax = 5ax + -1ax2 + 5b + -1bx + -5ax + 5x2

Reorder the terms:
125 + -5ax = 5ax + -5ax + -1ax2 + 5b + -1bx + 5x2

Combine like terms: 5ax + -5ax = 0
125 + -5ax = 0 + -1ax2 + 5b + -1bx + 5x2
125 + -5ax = -1ax2 + 5b + -1bx + 5x2

Add 'ax2' to each side of the equation.
125 + -5ax + ax2 = -1ax2 + 5b + -1bx + ax2 + 5x2

Reorder the terms:
125 + -5ax + ax2 = -1ax2 + ax2 + 5b + -1bx + 5x2

Combine like terms: -1ax2 + ax2 = 0
125 + -5ax + ax2 = 0 + 5b + -1bx + 5x2
125 + -5ax + ax2 = 5b + -1bx + 5x2

Add '-125' to each side of the equation.
125 + -5ax + -125 + ax2 = 5b + -1bx + -125 + 5x2

Reorder the terms:
125 + -125 + -5ax + ax2 = 5b + -1bx + -125 + 5x2

Combine like terms: 125 + -125 = 0
0 + -5ax + ax2 = 5b + -1bx + -125 + 5x2
-5ax + ax2 = 5b + -1bx + -125 + 5x2

Reorder the terms:
-5ax + ax2 = -125 + 5b + -1bx + 5x2

Reorder the terms:
125 + -5ax + ax2 + -5b + bx + -5x2 = -125 + 5b + -1bx + 5x2 + 125 + -5b + bx + -5x2

Reorder the terms:
125 + -5ax + ax2 + -5b + bx + -5x2 = -125 + 125 + 5b + -5b + -1bx + bx + 5x2 + -5x2

Combine like terms: -125 + 125 = 0
125 + -5ax + ax2 + -5b + bx + -5x2 = 0 + 5b + -5b + -1bx + bx + 5x2 + -5x2
125 + -5ax + ax2 + -5b + bx + -5x2 = 5b + -5b + -1bx + bx + 5x2 + -5x2

Combine like terms: 5b + -5b = 0
125 + -5ax + ax2 + -5b + bx + -5x2 = 0 + -1bx + bx + 5x2 + -5x2
125 + -5ax + ax2 + -5b + bx + -5x2 = -1bx + bx + 5x2 + -5x2

Combine like terms: -1bx + bx = 0
125 + -5ax + ax2 + -5b + bx + -5x2 = 0 + 5x2 + -5x2
125 + -5ax + ax2 + -5b + bx + -5x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
125 + -5ax + ax2 + -5b + bx + -5x2 = 0

The solution to this equation could not be determined.

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